We know that
• The ball is dropped from 1600 meters high.
,• Each time it bounces 3/4 of its original height.
This situation creates a geometric sequence where the reason is 3/4. To find the first three terms of this sequence, we just have to multiply each term with 3/4. We know that the first term is 1600.
[tex]1600\cdot\frac{3}{4}=\frac{4800}{4}=1200[/tex]The second term is 1200 meters.
[tex]1200\cdot\frac{3}{4}=\frac{3600}{4}=900[/tex]The third term is 900.
To find an equation, we have to use the geometric sequence formula-
[tex]a_n=a_1\cdot r^{n-1}[/tex]Replacing the information we have the equation that represents the situation of this problem.
[tex]a_n=1600\cdot(\frac{3}{4})^{n-1}[/tex]At last, the height after 4 bounces is
[tex]900\cdot\frac{3}{4}=\frac{2700}{4}=675[/tex]The height of the third bounce is 675 meters.
[tex]675\cdot\frac{3}{4}=\frac{2025}{4}=506.25[/tex]Therefore, the height of the ball after 4 bounces is 506.25 meters.
